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Finding the Fourth Proportional to 206, 309 and 77.80

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Solution

The fourth proportional to 206, 309 and 77.80 is: 116.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    206 : 309 = 77.80 : x
  2. Step 2: Convert to fraction form
    206/309 = 77.80/x
  3. Step 3: Cross multiply
    206x = 309 × 77.80
  4. Step 4: Simplify right side
    206x = 24,040.20
  5. Step 5: Solve for x
    x = 24,040.20/206
  6. Step 6: Final answer
    x = 116.70

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.